Interpolation theorem for anisotropic net spaces

The paper studies the interpolation properties of anisotropic net spaces $N_{\bar{p},\bar{q}}(M)$, where $\bar{p}=(p_1, p_2)$, $\bar{q}=(q_1, q_2)$. It is shown that the following equality holds with respect to the multidimensional interpolation method $(N_{\bar{p}_0,\bar{q}_0}(M), N_{\bar{p}_1,\bar{q}_1}(M))_{\barθ,\bar{q}}=N_{\bar{p},\bar{q}}(M),\;\;\; \frac{1}{\bar{p}}=\frac{1-\barθ}{\bar{p}_0}+\frac{\barθ}{\bar{p}_1}.$

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